On the Space-time Cross Correlation of a (2, 2) Mimo Rayleigh Channel Model

This paper extends a recently proposed space-time model for Rayleigh fading to a 2 transmit, 2 receive antenna (2, 2) multiple-input multiple-output (MIMO) channel with arbitrary spatial separation at the transmitter and at the receiver. The space-time correlation function for a non-isotropic scatterer distribution around the receiver is derived for the arbitrary configuration as a further extension of a result for a (2, 2) MIMO radio channel with a non-isotropic scatterer but co-located receive antennas. INTRODUCTION The combination of temporal and spatial diversity are two effective means by which communication quality and associated system performance can be significantly improved in a rich-scattering wireless environment. Multiple-Input Multiple-Output (MIMO) radio channels are a proven means to utilise these means to improve communication quality and improve associated system performance. Without designing highly detailed system models, which can be used for individual channel realisations, it is possible to obtain simpler macroscopic system models with a variety of possible applications. One such scheme, based on a traditional Clarkes/Jakes model [1], has been proposed in [2], where a rich isotropic distribution of scatterers is assumed around the mobile station (MS), the receiver. No major scatterers are located around the base station (BS), the transmitter. Space-time correlation and space-frequency cross spectrum functions corresponding to this distribution were derived. This was extended to the case of a (2, NR), i.e. 2 transmit, NR receive antennas, Rayleigh fading channel with a non isotropic distribution of scatterers in [3], where the receive antennas are co-located. One major drawback of [2, 3] is that they do not allow consideration of spatial separation at the receive antennas. Thus, they are not applicable to many proposed mobile communication systems with spatial separation at the receive antennas. This paper will provide a useful generalisation of [3] that will mean the space-time model can be applied to spatial separation at the receiver in a microcellular/macrocellular fast fading scenario to analyse a 2 transmit, 2 receive (2,2) MIMO radio channel. This model can be applied to analyse frequency non-selective wireless scenarios for various mobile transport systems. SPACE-TIME CROSS CORRELATION FORMULATION Consider a (2,2) MIMO radio channel with 2 transmit antennas (Tx) located at p, p′ with no major scatterers, and 2 receive antennas (Rx) located at q, q′ immersed in a rich non-isotropic scattering radio scenario, where the spatial separation at the transmit and receive side is in azimuth only, and of an arbitrary number of wavelengths (λ). The discussion in this paper can be applied to either a microcellular or macrocellular fast fading radio scenario. Fig. 1 illustrates the MIMO transmission model between the transmitter and the receiver.